7. A particle, of mass 0.3 kg , is projected from a point \(O\) on horizontal ground with speed \(u\). The particle is projected at an angle \(\alpha\) above the horizontal, where \(\tan \alpha = 2\), and moves freely under gravity. When the particle has moved a horizontal distance \(x\) from \(O\), its height above the ground is \(y\).

1. Show that $$y = 2 x - \frac { 5 g } { 2 u ^ { 2 } } x ^ { 2 }$$ The particle hits the ground at the point \(A\), where \(O A = 36 \mathrm {~m}\).
2. Find \(u\), the speed of projection.
3. Find the minimum kinetic energy of the particle as it moves between \(O\) and \(A\). The point \(B\) lies on the path of the particle. The direction of motion of the particle at \(B\) is perpendicular to the initial direction of motion of the particle.
4. Find the horizontal distance between \(O\) and \(B\).